scholarly journals Small scale effect on linear vibration of buckled size-dependent FG nanobeams

2015 ◽  
Vol 6 (2) ◽  
pp. 587-598 ◽  
Author(s):  
Sima Ziaee
Keyword(s):  
Scale Effect ◽  
Small Scale ◽  
Linear Vibration ◽  
Size Dependent ◽  
Small Scale Effect

Small-scale effect on the mechanical properties of metallic nanotubes

2012 ◽  
Vol 101 (9) ◽  
pp. 093109 ◽  
Author(s):  
Jin Zhang ◽  
Chengyuan Wang ◽  
Rajib Chowdhury ◽  
Sondipon Adhikari
Keyword(s):  
Mechanical Properties ◽  
Scale Effect ◽  
Small Scale ◽  
Small Scale Effect

The Small Scale Effect on Linear Vibration of Beam-Like Nanostructures

2012 ◽  
Vol 446-449 ◽  
pp. 3432-3435
Author(s):  
Cheng Li ◽  
Lin Quan Yao
Keyword(s):  
Axial Load ◽  
Vibration Mode ◽  
Multiple Scales ◽  
Separation Of Variables ◽  
Classical Mechanics ◽  
Small Scale ◽  
Transverse Displacement ◽  
Linear Vibration ◽  
Small Scale Effect ◽  
Multiple Scales Analysis

Transverse free dynamics of a beam-like nanostructure with axial load is investigated. The effects of a small size at nano-scale unavailable in classical mechanics are presented. Explicit solutions for natural frequency, vibration mode and transverse displacement are obtained by separation of variables and multiple scales analysis. Results by two methods are in close agreement.

Small Scale Effect on Boundary Conditions of Cantilever Single Carbon Nanotubes

2013 ◽  
Vol 275-277 ◽  
pp. 33-37
Author(s):  
Ming Li ◽  
Hui Ming Zheng ◽  
Luo Xia ◽  
Liu Yang
Keyword(s):  
Carbon Nanotubes ◽  
Boundary Condition ◽  
Boundary Conditions ◽  
Scale Effect ◽  
Nonlocal Elasticity ◽  
Small Scale ◽  
Euler Beam ◽  
Local Boundary ◽  
Local Boundary Condition ◽  
Small Scale Effect

In this paper, the boundary condition on free vibration of cantilever single-walled carbon nanotubes (SWCNTs) with Winkler elastic medium is investigated. The Euler beam theory with nonlocal elasticity is modeled as SWCNT. The analytical solution is derived and the numerical results show that the additional boundary conditions from small scale do not change natural frequencies. The reason is that the additional work made by the moment and shear force at the free end from small scale effect cancel each other, the boundary conditions due to local elasticity and nonlocal elasticity are also equivalent. Thus for simplicity, one can apply the local boundary condition to replace the small scale boundary condition.

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